Leading 3-1 from the first leg, Unai Emery's men were rarely troubled and their progression was never in doubt once captain Vicente Iborra rolled into an unguarded net.
Giovani dos Santos netted a stunning free-kick to give Villarreal something to shout about with 17 minutes to go.
But the hosts were effective on the counter and Denis Suarez's header killed off any visiting hopes of a memorable comeback, after Villarreal defender Eric Baill had been shown a second yellow card.
A fifth-straight win in this season's competition has the holders looking in good shape, but Villarreal will have a chance for revenge when they host an immediate rematch in this weekend's La Liga action.
Sevilla failed to replicate the blistering start they made to last week's first leg when they took the lead after just 13 seconds, but they still looked the more purposeful during the early exchanges at a rain-lashed Estadio Ramon Sanchez Pizjuan, Iborra twice going close.
Mario Gaspar and Tomas Pina mustered Villarreal efforts on goal, both of which were comfortably dealt with by Sevilla goalkeeper Sergio Rico.
The visitors did start to force their way into the game as the half wore on, but they continued to look vulnerable out wide and only a last-ditch intervention from Ivorian defender Bailly prevented Sevilla from taking the lead just before the break.
With the hosts content to sit back and hit on the counter, Villarreal found it increasingly difficult to find a way through in the second-half and when Mario and Pina did manage to find another sight of goal, Rico was again equal to their efforts.
As they continued to commit bodies forward in a desperate attempt to salvage their European dream, Marcelino's men inevitably left gaps at the back and they were hit with a classic sucker-punch on 69 minutes.
Colombian striker Carlos Bacca has been Sevilla's main goalscorer this season, but he turned provider on this occasion, timing his run perfectly as the visitors' defence pushed up and then squaring unselfishly for Iborra to side-foot home from close range.
To their credit, Villarreal responded almost immediately, Dos Santos bending a superb free-kick around the wall and into the far corner of Rico's net.
But it came too late in the day to be anything more than a consolation for the men in yellow, especially when the overworked Bailly received his marching orders after tangling with Iborra on 75 minutes.
Substitute Suarez iced the cake for Sevilla when he headed home their second goal 10 minutes later, confirming a place in the last eight for the Andalusians and striking a potentially significant psychological blow ahead of their crunch La Liga clash with the same opponents this coming weekend.
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